Research On Fast Electromagnetic Scattering Algorithm Of Finite Period Structure

The periodic structure has an extensive applications in microwave engineering,such as frequency selective surfaces,array antennas,photonic band gaps,and electromagnetic band gaps.Therefore,the fast and accurate analysis of finite-period structures has always been a hot topic in the society of computing electromagnetics.Although conventional numerical methods can be used to analyze finite periodic structures,they usually do not deal with finite periodic structures effectively,which leads to low efficiency.This thesis presents a fast and accurate method to solve the scattering problem of finite period electromagnetic structures.This algorithm can not only reduce the storage of impedance matrix,but also improve the computational efficiency.Theoretical research shows that the storage complexity of this algorithm is O(N),and the computational complexity is O(N log N).In addition,this algorithm does not bring additional errors.This method can deal with not only metal problems,but also complex media problems.It can be applied to both the surface integral equation and the volume integral equation.Firstly,in the third chapter,this thesis introduces the Mo M(method of moments)of electromagnetic scattering of metal targets,deduces the relevant formula of electric field integral equation,and also gives the processing method of singular terms of impedance matrix elements.Then,this thesis focuses on the electromagnetic scattering problem of finite periodic structures,and establishes a new method to improve the efficiency of the method of moments by using the fast Fourier transform method.Based on the geometrical repeatability of finite periodic structures and the translational invariance of green’s function,the fast Fourier algorithm for 1D finite periodic structures is studied and improved,and a new fast Fourier algorithm for electromagnetic scattering of 2D and 3D finite periodic structures is proposed.The basic principle is to convert the method of moments impedance matrix into a Toeplitz matrix and a cyclic matrix,which not only can significantly reduce the amount of storage,but also use the fast Fourier transform to calculate the matrix vector product.Compared with the traditional method of moments,this algorithm has obvious advantages in both memory usage and computing time.Compared with the AIM(Adaptive Integration Method)and FMM(Fast Multipole Method),the algorithm in this thesis does not introduce additional numerical errors.In the fourth chapter,a new algorithm combining fast Fourier transform and higher order basis function is proposed,which further improves the efficiency of the algorithm.It can effectively reduce the number of unknowns on the premise of maintaining high precision,thus further improving the efficiency of the algorithm in third chapter and reduce memory usage.In order to solve the electromagnetic problems of finite periodic structure of complex media,in the fifth chapter,a new idea of combining fast Fourier transform with discontinuous Galerkin method is proposed,and the corresponding formula is derived.The basic principle is to use the principle of volume equivalent to establish an integral equation based on the discontinuous Galerkin method.The piecewise constant vector basis function is defined inside the tetrahedral mesh,and then the repeating property of the periodic structure and the translation invariance of the Green’s function are used to obtain the fast Fourier algorithm.This algorithm can not only deal with multi-media and multi-scale media scattering problems flexibly and freely,but also has the advantages of less memory storage and high computational efficiency.